Suitable weak solutions and low stratification singular limit for a fluid particle interaction model
Suitable weak solutions and low stratification singular limit for a fluid particle interaction model
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DOI：
10.1090/s0033-569x-2012-01310-2
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发表时间：
2012-09
影响因子：
0.8
通讯作者：
J. Ballew;K. Trivisa
中科院分区：
文献类型：
--
作者：
J. Ballew;K. Trivisa
本文讨论了物理空间Ω⊂R中分散在粘性可压缩流体中的粒子演化的流粒相互作用模型。该系统由粒子演化的连续性方程、动量平衡和所谓的Smoluchowski方程表示。分散相和致密相之间的耦合是通过作用-反应原理流体和颗粒相互作用的阻力来实现的。利用Dafermos和DiPerna的相对熵方法，在对初始数据、物理域和外势作合理的物理假设下，给出了适当弱解的全局时间存在性。此外，对于有界域和无界域，严格地建立了系统的低马赫数和低层结极限。
This article deals with a fluid-particle interaction model for the evolution of particles dispersed in a viscous compressible fluid within the physical space Ω ⊂ R. The system is expressed by the continuity equation, the balance of momentum and the so-called Smoluchowski equation for the evolution of particles. The coupling between the dispersed and dense phases is obtained through the drag forces that the fluid and the particles exert mutually by the action-reaction principle. Using the relative entropy method of Dafermos and DiPerna, the global-in-time existence of suitable weak solutions is presented under reasonable physical assumptions on the initial data, the physical domain, and the external potential. In addition, the low Mach number and low stratification limits of the system are established rigorously for both bounded and unbounded domains.